She will face Democrat Ryan Greene for a chance at the job her father, former Vice President Dick Cheney, first won 40 years ago

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Liz Cheney speaks during a campaign appearance in Casper, Wyo, in this Wednesday, July 17, 2013 file photo.

Liz Cheney has won Wyoming's Republican primary for U.S. House, rebounding from her first unsuccessful congressional run in 2014.

In the general election she will face political newcomer Ryan Greene, who beat Charlie Hardy, a retired Roman Catholic priest, for the Democratic nomination.

In the race for the GOP nomination, Cheney beat seven challengers for a chance at the job her father, former Vice President Dick Cheney, first won 40 years ago.

Her campaign focused on national security and rolling back federal regulations affecting Wyoming's beleaguered coal industry.

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She was by far the best-funded candidate and brought in more than $1.5 million through July. Weeks before the primary, Cheney had almost 10 times more money than her next three opponents combined.

Her competitors included state Rep. Tim Stubson and state Sen. Leland Christensen.

And Cheney, of course, also has top name recognition. She has used her contacts to raise money from prominent Republicans nationwide.

Registered Republicans outnumber registered Democrats in Wyoming more than 3-to-1, so the eight-way GOP primary likely will prove the most important vote in determining who will fill the seat. As of Aug. 1, there were roughly 143,000 GOP voters registered compared to some 42,000 Democrats, according to the state Bureau of Elections.

In the last election cycle, Cheney mounted an audacious challenge to incumbent Enzi. Many prominent Wyoming Republicans accused her of being a "carpetbagger" for running against the state's senior senator when she had only recently moved to Wyoming from Virginia. She quickly dropped out of the race.

Now more seasoned, Cheney is undertaking the considerably less daunting task of running for an open seat.

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Cheney, a former Fox News commentator and State Department official, is emphasizing in her current campaign that she wants to represent Wyoming to fight against Washington overreach, particularly against federal regulation of the state's sagging coal industry. And echoing her father's criticism, she's been vocal in attacking President Barack Obama for actions she says have undermined national security.

Although Cheney emphasizes her family has deep roots in the "Cowboy State," those roots still aren't deep enough for Jason Gilbert, a Cheyenne insurance agent.

"I think she should have run from Virginia," Gilbert said Tuesday outside a polling place. "I know that she's got a name and she's got some recognition, but I don't know that there's much she's done for the state of Wyoming."

Gilbert said he voted instead for Darin Smith, an attorney and Christian Broadcasting Network executive from Cheyenne.

Dick Cheney was elected five times to the U.S. House seat for Wyoming that his daughter is now seeking. But his legacy cuts both ways. Many Democrats have decried Cheney's orchestration of the 2003 U.S. invasion of Iraq, calling it a disastrous foreign policy decision.

Tony Henry of Cheyenne said Tuesday he switched his party registration from Democrat to Republican specifically so he could vote against Liz Cheney. Henry said he voted for State Sen. Leland Christensen, of Alta, a former sheriff, county commissioner and U.S. Army special operations forces soldier.